Development of a mathematical model for the cooling channel of a liquid propellant rocket engine’s chamber with respect for variations in coolant density

This study focuses on the processes occurring within the cooling channels of a liquid rocket engine chamber. It is important to note that, from a design-stage efficiency prediction perspective, the cooling system is the most critical part of the engine chamber. This is because it cannot be tested without costly and labor-intensive fire tests. Therefore, mathematical models of heat transfer and fluid dynamics must describe accurately all processes taking place in the chamber. The study emphasizes accounting for the change in the density of the propellant component within the cooling channels. To verify the importance of this issue, an analysis was conducted on the changing parameters of the propellant components in the cooling channels of an engine. The assessment revealed that even when using high-boiling propellant components and moderate heating in the cooling channels, density changes can exceed 25 %. This paper presents the results of developing a model for the flow of propellant in the cooling channels of a liquid rocket engine chamber, taking density changes into account. The model builds on a cooling channel model previously developed by the authors. An equation that accounts for density variations was derived using established principles of fluid mechanics. Using the developed mathematical model, test calculations were performed, and the simulation results were compared with and without considering density changes. Furthermore, a comparison was conducted with calculated data available in the literature on heat transfer in the RD107 engine chamber, revealing an error margin of no more than 1.5 %. The resulting mathematical model may be recommended for use in the design of new rocket engine chambers with regenerative cooling